Final thoughts (100 years, part VII)

To end my series of posts on the man and the book (D’Arcy Thomspon and On Growth and Form respectively, the latter a book with over 1000 pages), I wanted to share a few more quotes from and about him that I found interesting enough to type out:

“In his figure and bearded face there was majestic presence; in is hospitality there were openness, kindness and joviality; in his ever quick wit were the homely, the sophisticated and, at times, the salty… in status he became a very doyen among professors the world over; in his enquiring mind he was like those of whose toungue and temper he was a master, the Athenians of old, eager ‘to tell or hear some new thing'” – Professor Peacock (1)

  1. With the name Professor Peacock, I can’t help but imagine a flamboyant, multicolour-labcoat-wearing, frizzle-haired man…
  2. I hope the meaning of the word salty has changed over time…

There is a certain fascination in such ignorance; and we learn without discouragement that Science is “plutot destine a etudier qu’a connaitre, a chercher qu’a trouve la verite.” (2)
(Rather than destined to study for knowledge, (we are) searching to find the truth.)


In my opinion the teaching of mechanics will still have to begin with Newtonian force, just as optics begins in the sensation of colour and thermodynamics with the sensation of warmth, despite the fact that a more precise basis is substituted later on. (3)

As a self-proclaimed science communicator, it is often difficult to judge how much to simplify things. On the other hand, making things relatable to everyday experiences does not necessarily mean telling untruths. Classical physics may not be valid for every single situation, but it is often enough to describe what is happening without needing to resort to more complicated relative physics. And you don’t have to start quoting wavelengths when a colour description would do just as well. Fill in the details later, if necessary.

Some quotes on evolution and natural selection:

And we then, I think, draw near to the conclusion that what is true of these is universally true, and that the great function of natural selection is not to originate, but to remove. (4)

Unless indeed we use the term Natural Selection in a sense so wide as to deprive it of any purely biological significance; and so recognise as a sort of natural selection whatsoever nexus of causes suffices to differentiate between the likely and the unlikely, the scarce and the frequent, the easy and the hard: and leads accordingly, under the peculiar conditions, limitations and restraints which we call “ordinary circumstances,” one type of crystal, one form of cloud, one chemical compound, to be of frequent occurrence and another to be rare. (5)

We can move matter, that is all we can do to it. (6)

On a fundamental level, are we really able to build things? Aren’t we just rearranging the building blocks?

I know that in the study of material things, number, order and position are the threefold clue to exact knowledge; that these three, in mathematician’s hands, furnish the “first outlines for a sketch of the universe“, that by square and circle we are helped, like Emile Verhaeren’s carpenter, to conceive “Les lois indubitable et fecondes qui sont la regle et la clarte du monde.” (7)

(The unquestionable and fruitful laws that rule and clarify the world.)

For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty. (8)

Delight in beauty is one of the pleasures of the imagination … (9)

#MathIsLife. Thank you, D’Arcy, for the 1000+ pages of mind-expanding, educational and philosophical topics.



(1) D’Arcy Thompson and his zoology museum in Dundee – booklet by Matthew Jarron and Cathy Caudwell, 2015 reprint

(2) On Growth and Form – p. 19

(3) Max Planck

(4) On Growth and Form – p. 269-270

(5) On Growth and Form – p. 849

(6) Oliver Lodge

(7) On Growth and Form – p. 1096

(8) On Growth and Form – p. 1096-1097

(9) On Growth and Form – p. 959

(2, 4-6, 8-9) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)

When size matters (100 years, Part VI)

Neat process diagrams of metabolism always gave the impression of some orderly molecular conveyer belt, but the truth was, life was powered by nothing at the deepest level but a sequence of chance collisions. (1)

Zoom down far enough (but not too far – or the Aladdin merchant might complain) and all matter is just a soup of interacting molecules. Chance encounters and interactions, but with a high enough probability to happen. In essence, life is a series of molecular interactions (that, in turn, are atomic interactions and so on and so on…)

The form of the cellular framework of plants and also of animals depends, in its essential features, upon the forces of molecular physics. (2)

Quite often, we can ignore those small-scale phenomena, but only as long as the system we are describing is large enough. As in physics, in biological systems size does matter (*insert ambiguous joke here*). We have to adapt the governing physical rules depending on the scale that we are observing. Do we consider every quantum-biological detail, can we use a cell as the smallest entity or even use whole organisms as the smallest functional entity?

Life has a range of magnitude narrow indeed compared to with which physical science deals; but it is wide enough to include three such discrepant conditions as those in which a man, an insect and a bacillus have their being and play their several roles. Man is ruled by gravitation, and rests on mother earth. A water-beetle finds the surface of a pool a matter of life and death, a perilous entanglement or an indispensable support. In a third world, where the bacillus lives, gravitation is forgotten, and the viscosity of the liquid, the resistance defined by Stoke’s law, the molecular shocks of the Brownian movement, doubtless also the electric charges of the ionised medium, make up the physical environment and have their potent and immediate influence on the organism. (3)

Observing life at the smallest scales (by which I mean cells and unicellular organisms) at least has the advantage the rules driving form and structure can, at least in many cases, be considered relatively simple: surface-tension.

In either case, we shall find a great tendency in small organisms to assume either the spherical form or other simple forms related to ordinary inanimate surface-tension phenomena, which forms do not recur in the external morphology of large animals. (4)

While on the topic of size, as many things in the universe: size is relative. I have noticed in conversations with colleagues and supervisors that what is considered small or large, definitely depends on the point of perspective (and often: whatever the size is that that person typically studies). I could assume that for a zoologist, a mouse is a small animal, but tell a microscopist they have to image an area of 1 mm² and the task seems monstrous. For a particle physicist, a micrometre is immense, but for an astrophysicist, the sun is actually quite close.

We are accustomed to think of magnitude as a purely relative matter. We call a thing big or little with reference with what it is wont to be, as when we speak of a small elephant of a large rat; and we are apt accordingly to suppose that size makes no other or more essential difference. (5)

Undoubtedly philosophers are in the right when they tell us that nothing is great and little otherwise than by comparison. (6)

There is no absolute scale of size in the Universe, for it is boundless towards the great and also boundless towards the small. (5)

That’s the amazing thing about science: we strive to understand the universe on all scales. The universe is mindblowing in its size, in both directions on the length scale.

We distinguish, and can never help distinguishing, between the things which are at our own scale and order, to which our minds are accustomed and our senses attuned, and those remote phenomena which ordinary standards fail to measure, in regions where there is no habitable city for the mind of man. (7)

Good thing we have scientists, amazing minds, capable of studying, visualising and even starting to understand the universe on all its scales…

My mind might be boggled, but here’s a man that looks like his mind contains the universe. (D’Arcy in his 80s)

(1) Permutation city – Greg Egan, p. 67

(2) Wildeman

(3) On Growth and Form – p. 77

(4) On Growth and Form – p. 57

(5) Gulliver

(6) On Growth and Form – p. 24

(7) On Growth and Form – p. 21

(3-4, 6-7) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)

Let’s get physical (100 years, Part V)

[…] of the construction and growth and working of the body, as of all else that is of the earth earthy, physical science is, in my humble opinion, our only teacher and guide. (1)

You might have seen the xkdc comic ranking different scientific disciplines by their purity (and if you haven’t, it’s just a bit of scrolling away). The idea it portrays is that all sciences are basically applied physics (which is in turn applied mathematics). In other words: if you go deep enough to a subject, you eventually end up explaining in with principles from physics. And this is the same principle D’Arcy explores in his book. That has over 1000 pages, did you know that?


A famous D’Arcy quote states that the study of numerical and structural parameters are the key to understanding the Universe:

I know that the study of material things number, order and position are the threefold clue to exact knowledge, and that these three, in the mathematician’s hands, furnish the ‘first outlines for a sketch of the Universe.’ (2)

You can ask the average high school student about mathematics, and the usual response would probably be something in the lines of: “Ugh, I’ll never use this for anything.” Sometimes, it might be difficult to see the every-day use of mathematics, or even the not-so-everyday use. But in reality, the possibilities are endless (given that we are open to having long lists of endless equations that need a supercomputer to solve – probably).

We are apt to think of mathematical definitions as too strict and rigid for common use, but their rigour is combined with all but endless freedom. The precise definition of an ellipse introduces us to all the ellipses in the world; the definition of a ‘conic section’ enlarges our concept, and a ‘curve of higher order’ all the more extends our range of freedom.

It might not be straightforward to see how mathematics (or physics for that matter) would help a biologist in the understanding of natural processes. However, there are a few examples of how physical properties, forces or phenomena are used in biology, such as helping bone repair:

The soles of our boots wear thin, but the soles of our feet grow thick the more we walk upon them: for it would seem that the living cells are “stimulated” by pressure, or by what we call “exercise,” to increase and multiply. The surgeon knows, when he bandages a broken limb, that his bandage is doing something more than merely keeping the part together: and that the even, constant pressure which he skilfully applies is a direct encouragement of the growth and an active agent in the process of repair. (4)

Nowadays the link between physics and biology is more accepted that a century ago, leading to new research fields such as biomechanics, mechanobiology and “physics of cancer”. I have eluded to some of the links between cancer and physics in previous posts (Physics of Cancer, Part I and II). Mathematical models are commonly used to better understand biological processes, including signalling pathways, tissue formation and growth and changes occurring in cancer.

This goes to show (again) that “interdisciplinary” is not just a fancy buzzword, it is a core principle of scientific research. While I must admit from own experience that carrying out interdisciplinary research might not be the easiest path, the potential discoveries and applications are even more endless. And while it might seem mind-boggling, I would argue that mind-bogglement is a good thing, stretching the potential of our minds and our understanding of the universe. And as far as I can read, D’Arcy agrees:

… if you dream, as some of you, I doubt not, have a right to dream, of future discoveries and inventions, let me tell you that the fertile field of discovery lies for the most part on those borderlands where one science meets another. There is a cry in the land for specialisation … but depend on it, that the specialist who is not reinforced by a breadth of knowledge beyond his own speciality is apt very soon to find himself only the highly trained assistant to some other man … Try also to understand that though the sciences are defined from one another in books, there runs through them all what philosophers used to call the commune vinculum, a golden interweaving link, to their mutual support and interpretation. (5)

So I guess my point is (if there even was a point in this post, apart from that the book has like over 1000 pages, in case you didn’t know): if you are a biologist, don’t be afraid to break some sweat and get physical. And the opposite goes for physicists. You might want to get a bit chemical as well, while you’re at it.

The Homo Universalis is back!

Featured image: math and shells.

(1) On Growth and Form, p 13.

(2) On Growth and Form, p. 1096

(3) On Growth and Form, p. 1027

(4) On Growth and Form, p. 985

(5) D’Arcy Thompson and his zoology museum in Dundee – booklet by Matthew Jarron and Cathy Caudwell, 2015 reprint

(1-4) from D’Arcy Thompson, On Growth and Form,  Cambridge university press, 1992 (unaltered from 1942 edition)